AU2011261169B2

AU2011261169B2 - Optimising objectives of a plant and a carbon dioxide capture facility

Info

Publication number: AU2011261169B2
Application number: AU2011261169A
Authority: AU
Inventors: Trent Liam Harkin; Andrew Forbes Alexander Hoadley
Original assignee: KC8 Capture Technologies Ltd
Current assignee: KC8 Capture Technologies Ltd
Priority date: 2010-06-02
Filing date: 2011-06-02
Publication date: 2017-03-02
Anticipated expiration: 2031-06-02
Also published as: AU2011261169A1; WO2011150462A1

Abstract

The present invention relates to a method and system for optimising objectives of a plant and a carbon dioxide capture facility. The method comprises a multi-objective algorithm and includes the use of process simulation packages and linear programming programs to optimise objectives. The objectives may include an optimal configuration for capturing carbon dioxide from emissions of a power plant via the carbon dioxide capture facility.

Description

1

A METHOD AND SYSTEM

FIELD OF THE PRESENT INVENTION

The present invention relates to a method and system for optimising objectives of a plant and a carbon dioxide capture facility.

BACKGROUND OF THE INVENTION

Carbon dioxide capture and storage (CCS) is expected to become one of the main techniques for reducing carbon dioxide emission to the atmosphere. One of the advantages of CCS is that it can be included in new plants or readily retrofitted to existing plants, however, in either situation the provision of CCS is usually associated with an energy cost and/or reduction in production of the primary product such as electrical power, steel, concrete and so forth. The feasibility of CCS is presently investigated on case-by-case basis using a range of different criteria. The present invention relates to a method and system that can provide information on the costs and benefits of capturing carbon dioxide so that the feasibility of particular projects can be more easily analysed.

For example, in the case where carbon dioxide is captured from a flue gas stream of a coal fired power station, and the energy required for operation of the carbon dioxide capture is obtained from the power station, an embodiment of the present invention can provide information such as the impact of capturing carbon dioxide on a range of objectives such as, but by no means limited to, the power output generated by the power plant.

SUMMARY OF THE INVENTION

According to the present invention, there is provided a method of optimising a power plant combusting fuels to raise steam to generate power and a carbon dioxide capture facility which captures carbon dioxide from the power plant using a multi-objective optimisation algorithm, the method comprising: a) selecting one or more variables relating to the plant and the carbon dioxide capture facility, each variable comprising a range of values, wherein the variables selected for the power plant are temperature and pressure of the steam raised by the power plant, and the variables of the carbon dioxide capture facility is an amount of energy utilised by the carbon dioxide capture facility; b) applying the multi-objective optimisation algorithm to determine a population of individuals, where each individual includes a set of values for each variable within respective ranges of values; 8712584_1 (GHMatters) P83932.AU.1 2 2011261169 13 Feb 2017 10 15 20 25 c) determining operating conditions of the plant and the carbon dioxide capture facility by conducting process and heat integration analysis on selected streams of the power plant and the carbon dioxide capture facility by comparing differentials in energy supply and energy demands over temperature levels based on the determined sets of values of the individuals and calculating a selected objective which includes a minimum of the amount of energy utilised by the carbon dioxide capture facility and thereby taken from the power plant according to the following equations k Minimise = =w (5) i=1 and subject to the : 'y'.fjhj.Tton - GCCTton (6) i= 1 V t = 2, 3,...j YfA^GCQ+Q^ (7) i= 1 wherein k Number of steam extraction points j Number of temperature intervals f. Mass flowrate of the steam exiting the ith section of the turbine (kg/s) □i Specific amount of power generated by the turbine from steam at the turbine section i to the outlet of the turbine (kJ/kg) w Turbine power that could be generated with the steam utilised from all extraction points (kW) hijt Enthalpy available in steam i between the steam at temperatures t and the turbine outlet, if t is greater than the steam supply temperature then it is the difference from the supply temperature down to the turbine outlet (kJ/kg) t the temperature interval in the combined list of temperatures in the GCC and the SCC (1 = Hottest temperature (Ttop), m = pinch point temperature) Ttop The hottest temperature in the GCC or SCC GCC, Energy in the grand composite curve at temperature t Qxs The excess energy in the SCC above that required to meet the heat duty (kW) d) comparing and outputting the minimum of the amount of energy utilised by the carbon dioxide capture facility determined in step c) and thereby taken from the power plant and 8712584_1 (GHMatters) P83932.AU.1 3 e) configuring the plant and the carbon dioxide capture facility so as to operate in accordance with the operating conditions determined in step c).

The optimised objective may be obtained when no further improvement of the objectives can be obtained.

The method may include a preliminary step of selecting one or more objectives to be optimised, and suitably, when the multi-objective optimisation algorithm is used to maximise or minimise the objective(s). The objective selected may relate to objectives of either one or both of the plant and the carbon dioxide capture facility. An example of an objective of the carbon capture facility is the amount of carbon dioxide captured. An example of an objective of the plant when in the form of a power station is the loss in production of the plant as result of the amount of carbon dioxide captured.

The multi-objective optimisation algorithm may be any variety of algorithm that optimises multiple objectives. An example of a suitable multi-objective optimisation algorithm is a MOO algorithm developed by G.P.Rangaiah of the National University of Singapore. It will be appreciated that other multi-objective optimisation algorithms may be used such as vector evaluated genetic algorithms (VEGA™), Multi-objective genetic algorithm (MOGA™), niched Pareto genetic algorithm (NPGA™), Improved strength pareto evolutionary algorithm (SPEA2™), region-based selection in evolutionary multi-objective optimization (PESA-II™) and Rank density based genetic algorithm (RDGA™).

The variables selected in step a) may include any one or a combination of the following: • variables that effect operating condition of the plant; • variables that effect operating conditions of the carbon dioxide capture facility; • variables that are a function of capital cost of the plant; • variables that are a function of capital cost of the carbon dioxide capture facility.

In the situation in which step a) includes selecting multiple variables, for example x number of variables and a population size of n individuals, steps b) and c) may be performed n number of times whereby separate sets of values for each variable within respective ranges of values are determined, and in turn, a respective objective is determined.

The method may be iterative whereby the objectives determined in step c) are compared in step d) with the determined objectives of previous iterations, and based on the comparison, the method includes repeating steps b) to d) a predetermined number of times or until a difference between the objectives of consecutive iterations is minimised or within an acceptable deviation margin. In an example, the method compares the objectives for 8712584_1 (GHMatters) P83932.AU.1 4 each of the n individuals determined by one of the iterations, with the best results of objectives determined in previous iterations to determine the optimised objectives. In our experience, an acceptable deviation margin can be achieved when by at least 40 iterations, suitably from 50 to 100 iterations, and in some application from 50 to 1000 iterations. The acceptable margin will depend on the objective and the variables that impact on the objective.

In the situation in which the objectives are outside the acceptable margin, steps b) to d) may be repeated using the population set of values having a corresponding objective that is the closest to the optimised objective. In an example, each iteration of determined objectives is compared with previous iterations and those iterations determined to be closer to the optimised objective replace the previous iterations for subsequent comparison.

In the situation in which steps b) to d) are being carried out for a first iteration, the population set of the values for the variables may be randomly generated.

In the situation in which steps b) to d) are being repeated in a subsequent iteration, the multi-objective optimisation algorithm may regenerate a revised population set of values for the variables. Even more suitably, the revised population set of values are generated by the multi-objective optimisation algorithm that favours the objectives based on previously determined objectives. Ideally, the objectives favoured are those that either maximise or minimise the objectives.

Step c) may include simulating operating conditions of the plant and carbon dioxide capturing facility using process simulation software, for instance software commercially available under the trade names AspenPlus™, Hysys™, and Pro II™.

Simulating the operating conditions of the plant and the carbon dioxide capturing facility may include matching the selected variables of step a) with inputs of the software simulation and changes in the population set of the values for each variable are used to make changes to the input variables of the simulation. For example, in the situation were the variables include the lean loading of a solvent solution fed to an absorber, an input of the simulation is the lean solvent loading entering the absorber and the stripper needs to be configured to attain the specified lean solvent loading.

Step c) may include conducting process and heat integration analysis, including thermodynamic analysis, on selected streams of the plant and the carbon dioxide capture facility by comparing differentials in energy supply and energy demands over temperature levels.

Step c) may include conducting heat pinch analysis on selected streams of the plant and the carbon dioxide capture facility to provide a grand composite curve that identifies either one or a combination: 8712584J (GHMatters) P83932.AU.1 5 i) energy sources within the plant and carbon dioxide capture plant; and ii) energy demands to run the plant and carbon dioxide capture plant.

The selected streams may be all of the hottest streams and all of the coldest streams, or a subset of the hottest and the coldest streams if some streams are better omitted from the pinch analysis.

The pinch analysis may involve matching the energy sources and demands such that the temperature of the energy source is at least a specified temperature difference greater than the energy demand. The pinch analysis can be carried out manually, but is suitably carried out by way of standard software programs implemented using Excel, visual basic, Matlab or any number of programming languages.

Step c) may further include applying a linear programming algorithm to maximise or minimise the objective(s) as function of the grand composite curve provided by the pinch analysis.

The linear programming algorithm may be based on a linear relationship between key variables of the plant. For example, the key variable may be the pressure of steam, or pressure levels of steam, from a boiler of the coal fired plant that is available for use in the carbon dioxide capture facility. In another example, the key variable may be the temperature and/or pressure of steam available from the hood of the steel smelter, or any other boiler of a steel smelter.

The method may include outputting the optimised objectives of the plant and the carbon dioxide capture facility. For example, the output may be a graphical representation the objective such as, but by no means limited to a bar-chart, pie-chart or curve.

It is within the scope of the present invention that the plant may be any plant, but by no means limited to an industrial plant, pilot plant, or replica plant or a part thereof that generates, handles, and treats carbon dioxide. For example, the plant may be a power station which combusts fossil fuels such as coal, oil or natural gas in air or in enriched oxygen, known as oxyfuel, or fuels derived therefrom such as synthesis gas and LNG. The power station may also combust other hydrocarbon fuels such as bio-fuels and other renewable fuels. In another example, the plant may be a fuel production plant such as an oxyfuel production plant, a gasification plant or a natural gas production plant. In yet another example, the plant may be a cement or steel production plant in which a fuel is combusted in the production of a product.

The carbon dioxide capturing facility may be carried out using any technology that reduces carbon dioxide emissions to the atmosphere. The carbon dioxide capturing facility may also be used for capturing carbon from any stream within a plant including, but by no means limited to, a pre-combustion, post-combustion or oxyfuel gas stream. For example, 8712584_1 (GHMatters) P83932.AU.1 6 the carbon dioxide facility may involve the use of any capturing technology which includes, but is by no means limited to, solvent extraction, membrane separation, physical and chemical adsorbents, low temperature hydrates or any other technique whereby carbon dioxide is captured or separated so as to reduce carbon dioxide emissions to the atmosphere. Once captured, the carbon dioxide may be used for any purpose including use in other industrial processes, mineral storage and subterranean storage in geological formations. In addition, the carbon dioxide capture facility may be used for capturing a range of acid gases including carbon dioxide, SOx and NOx. Moreover, the variables chosen may include the degree of capture of all acid gases including loading of acid gases in the solvent solution and alike.

The plant may be characterised by being a power plant, suitably a power plant combusting fossil fuels and the carbon dioxide capture facility captures carbon dioxide from a flue gas stream.

The carbon dioxide capture facility may be characterised as being a solvent absorption facility in which carbon dioxide is captured from the flue gas stream.

The objectives to be optimised may include, but are by no means limited to, any one or a combination of: • carbon dioxide captured; • energy required for regeneration of loaded solvent solution; • energy required for cooling the lean solvent solution; • energy required for cooling the gas stream produced in the stripper; • loading of carbon dioxide in the lean solvent solution fed to an absorber; • capital costs of the carbon capture facility; • power generated by the power plant • operating pressure of a stripper in which a loaded solvent solution is regenerated; • operating pressure of an absorber in which a lean solvent solution is loaded; • flowrate of the solvent solution; • energy required for creating a pressure differential across a gas absorption membrane for separating carbon dioxide; • energy required for operating a pressure swing adsorption facility; • cost of power generated from a power station; • profitability of a plant; and • return on investment of the plant. 8712584J (GHMatters) P83932.AU.1 7

The energy requirements mentioned in the above paragraph may be provided by energy sources or sinks from within the power station, or auxiliary energy sources that are separate from the power plant may provide all or only part of the energy requirements. For example, heat for regenerating the loaded solvent solution may be obtained from within the power station, or at least in part or solely from an auxiliary heating source or an auxiliary power source. In another example, the energy for cooling or operation of the pressure swing adsorption facility may be provided from within the power station, or at least in part or solely from an auxiliary cooling source or an auxiliary power source. In yet another embodiment, the energy required for creating a pressure differential across the gas absorption membrane may be provided from within the power station, or at least in part or solely from an auxiliary energy source.

The variables may include, but are by no means limited to, any one or a combination of the following: • the flowrate of a solvent solution for absorbing carbon dioxide from the flue gas stream; • the carbon dioxide loading of the solvent solution entering an absorber in which carbon dioxide is absorbed from the flue gas stream; • the acid gas loading e.g., SOx and NOx loading on the solvent solution; • operating pressure of a stripper in which loaded solvent solution is regenerated; • the temperature of the solvent solution entering the stripper; • the temperature of the flue gas stream; • the temperature of the solvent solution that has been regenerated in the stripper; • the volume or height of the stripper; • the volume or height of the absorber; • energy required to drying coal combusted in the power station; • energy required for carbon dioxide compression and/or storage; • energy required for creating a pressure differential across a gas absorption membrane for separating carbon dioxide; • residence time of a carbon dioxide rich stream in contact with a gas absorption membrane; • energy required for operating a pressure swing adsorption facility; • residence time of a carbon dioxide rich stream in contact with an adsorbent of a pressure swing adsorption facility; • operating pressure of the solvent absorber; • temperature level of the air pre-heat in a combustion process; and • pressure and temperature levels in a steam turbine.

The pinch analysis may include: i) creating a profile of the sum of the energy of the selected hot streams of the power plant and selected hot stream of the carbon capture facility; 8712584_1 (GHMatters) P83932.AU.1 - 8 - ii) creating a profile of the energy of selected cold streams of the power plant and selected cold stream of the carbon dioxide capture facility (i.e., composite curves); and iii) rationalising the profiles created in i) and ii) to provide a grand composite curve showing an amount of the surplus or shortfall in heat.

For example, the amount of heat may represent either a) required heat for operation of the carbon capture facility (such as regeneration of a loaded solvent solution), or b) available heat for the generating power in the power plant.

The simulation may include inputting information on stages of a steam turbine and/or stages of a boiler house of the plant.

Moreover, step c) may include assuming that energy for the carbon dioxide capture facility is available at, or over, a temperature range for regenerating a loaded solvent solution.

Step c) may include assuming that energy from steam of a boiler is available at a particular pressure or temperature.

Step c) may include applying the linear programming algorithm to maximise an amount of power that can be generated by the power plant for a given composite curve determined by the pinch analysis.

In the situation in which the plant and the carbon dioxide capture facility include an energy source having known amounts of energy over given temperature levels, and the linear programming algorithm can minimise the amount of energy utilised by the carbon dioxide capture facility and thereby taken from the plant as a function of the available energy at each temperature level.

For example, where the carbon dioxide capture facility is being retrofitted to an existing coal fired power plant, the steam levels of a plant may be known, and the linear programming algorithm can include the amount of steam available at each level. The lowest steam level is normally disregarded. When each steam extraction level is known i.e., temperature and pressure, the amount of energy “lost” for generating power (ie lost from the turbine of the plant) and the amount of energy available in the steam are both linear, the linear programming algorithm can be solved to minimise the amount of power “lost” from the turbine according to the following equations. objective 8712584_1 (GHMatters) P83932.AU.1 9 2011261169 13 Feb 2017 k

Minimise = =w (EQ 5) i=1 and subject to the : k Σ/Α** - GCCTiop i= 1 (EQ 6) V t = 2, 3,...j k Y f .h, < GCC + Q / J J l l,t t (EQ 7) i= 1 where k Number of steam extraction points j Number of temperature intervals f. Mass Flowrate of the steam exiting the ith section of the turbine (kg/s) □i Specific amount of power generated by the turbine from steam at the ίο 15 turbine section i to the outlet of the turbine (kJ/kg) w Turbine power that could be generated with the steam utilised from all extraction points (kW)

hijt Enthalpy available in steam i between the steam at temperatures t and the turbine outlet, if t is greater than the steam supply temperature then it is the difference from the supply temperature down to the turbine outlet (kJ/kg) t the temperature interval in the combined list of temperatures in the GCC and the SCC (1 = Hottest temperature (Ttop), j = pinch point temperature) Ttop The hottest temperature in the GCC or SCC GCCt Energy in the grand composite curve at temperature t

Qxs The excess energy in the SCC above that required to meet the heat duty (kW)

Equation 6 is a constraint which ensures that the amount of energy provided by the SCC is greater than the heat required by the GCC. Equation 7 is a series of constraints 25 which ensure that the available energy is adequate to achieve the required heating.

In the situation in which the plant and the carbon dioxide capture facility include an energy source having an unknown amount of energy, and the linear programming algorithm can maximise the amount of power generated by the plant as a function of the amount of energy available and the amount of energy used by the carbon dioxide capture facility. 30 For example, where the carbon dioxide capture facility and the plant, being a coal fired power plant are new, the amount of power generated by the plant can be maximised by the linear programming algorithm maximising the amount of steam available for generating 8712584_1 (GHMatters) P83932.AU.1 10 2011261169 13 Feb 2017 power in a turbine of the plant. In this case the linear program can maximise the amount of the power generated by solving the following equations. objective k 5 Maximise = =W (EQ 8) i=1 and subject to

Vt= 1...J (EO 9) i= 1 wherein F, Mass flowrate of the steam generated in the ith section of the turbine(kg/s) k Number of steam levels j The number of temperature intervals in the GCC and the SCC. 15 f. Mass flowrate of the steam extracted from the ith section of the turbine i Specific amount of power generated by the turbine from steam at the turbine section i to the outlet of the turbine (kJ/kg) W Turbine power that could be generated with the given steam generation and utilisation rates (kW)

Hijt Enthalpy of steam generated in steam level i at a temperature half the minimum temperature difference above the actual temperature (kJ/kg) hijt Enthalpy of the steam at extraction point i at a temperature half the minimum temperature difference below the actual temperature (kJ/kg) GCCt Energy in the grand composite curve at a temperature t.

According to the present invention there is also provided a system for optimising 25 objectives of a plant with a carbon dioxide capture facility using a multi-objective optimisation algorithm, the system comprising: a processor arranged to: receive selection of one or more variables relating to the plant and the carbon dioxide capture facility, each variable comprising a range of values; 30 apply the multi-objective optimisation algorithm to determine a population of individuals, where each individual includes a set of values for each variable within respective ranges of values; determine operating conditions of the plant and the carbon dioxide capture facility based on the determined individual set of values for each variable to 8712584_1 (GHMatters) P83932.AU.1 11 determine objectives of the plant and the carbon dioxide capture facility for each individual; compare the determined objectives of the plant and the carbon dioxide capture facility for each individual in the population set to determine the optimised objectives; and output the optimised objectives.

The present invention also relates to a computer program code which when executed implements the method as described in any one or combination of the above paragraphs.

The present invention also relates to a computer readable medium comprising the computer program code. The present invention also relates to transmitting the program code.

The present invention also relates to a data signal comprising the program code. The method of the present invention may also be implemented by a computer.

The present invention also relates to a method of optimising objectives of a plant and a carbon dioxide capture facility using a multi-objective optimisation algorithm, the method comprising: a) selecting one or more variables relating to the plant and the carbon dioxide capture facility, each variable comprising a range of values; b) applying the multi-objective optimisation algorithm to determine a population of values for each variable within respective ranges of values; c) determining operating conditions of the plant and the carbon dioxide capture facility based on the determined population set of values for each variable to determine objectives of the plant and the carbon dioxide capture facility for each variable; d) comparing the determined objectives of the plant and the carbon dioxide capture facility for each individual in the population set to determine optimised objectives; and e) outputting the optimised objectives.

BRIEF DESCRIPTION OF THE DRAWINGS

An embodiment of the present invention will now be described with reference to the attached drawings, of which:

Figure 1 a process flow diagram of a carbon dioxide capture facility in which a solvent solution is conveyed between an absorption column in which the solvent sorbs 8712584_1 (GHMatters) P83932.AU.1 12 carbon dioxide from a gas stream and a stripping column in which the solvent solution is regenerated; and

Figure 2 which is a block diagram illustrating in detail steps of a method including setting up a program and running the program for optimising one or more objectives of a plant and a carbon dioxide capture facility;

Figure 3 is a schematic illustration of a steam turbine model;

Figure 4 is a graph illustrating a Grand Composite Curve (GCC) and Steam composite Curve (SCC) for an existing power plant i.e., a retrofit;

Figure 5 is a graph illustrating a GCC and SCC for a new power plant;

Figure 6 is a graph illustrating the Pareto-optimal solutions for Case 1 a - Tight range and Case 1 b - Wide range of Example one;

Figure 7 is a graph illustrating the impact of the lean solvent loading on the reboiler energy of a power plant for Case 1a and 1b of Example one;

Figure 8 is a graph illustrating the correlation between solvent lean loading and flowrate for Case 1 a and 1 b of Example one;

Figure 9 is a graph illustrating the impact of stripper pressure on the Pareto-optimal solutions of the reboiler energy and capture rate for Case 2 of Example one;

Figure 10 is a graph illustrating the solvent loading and stripper pressure for the optimised points shown with the stripper reboiler energy for Case 2 of Example one;

Figure 11 is a graph illustrating optimal solutions for Case 3 without heat integration and Case 4 with heat integration of Example one;

Figure 12 is a graph illustrating solvent loading and stripper pressure for the Pareto-optimal solutions for Case 3 of Example one;

Figure 13 is a graph illustrating stripper pressure for the optimised points of Case 3 and 4 of Example one;

Figure 14 is a graph illustrating solvent loading for optimised solutions for Cases 2, 3 and 4 of Example one;

Figure 15 is a graph illustrating net power as a function of the capture rate for optimised solutions when optimising to maximise the net power (x) and when optimising to minimise the differential cost of electricity ( ) of Example two;

Figure 16 is a graph illustrating differential cost of electricity ( COE) as a function of the capture rate for optimised solutions when optimising to maximise the net power (x) and when minimising the COE ( ) of Example two;

Figure 17 is a graph illustrating capital costs as a function of capture rate for the optimisation case to maximise net power (x) and to minimise COE( )of Example two; and 8712584_1 (GHMatters) P83932.AU.1 13

Figure 18 is a graph illustrating solvent flowrate as a function of capture rate when optimised for minimum COE( )of Example two.

DETAILED DESCRIPTION

The steps illustrated in Figure 2 will be described and exemplified with reference to the carbon capture facility shown in Figure 1.

Figure 1 is an example of a process flow diagram of a carbon dioxide capture facility in which an absorbing medium in the form of a potassium carbonate solution is circulated. The carbon capture facility includes an absorber to which a lean solvent solution SOL1 is fed and from which loaded solvent solution SOL2 exits. The solvent solution sorbs carbon dioxide from a gas stream rich in carbon dioxide which is fed to the base of the absorber. A gas stream lean in carbon dioxide exits at the top of the absorber. The loaded solvent solution SOL2 is fed to a stripping column for regenerating the solvent via a recuperative heat exchanger that heats the loaded solvent SOL3 before entering the stripper. A reboiler provides heat to the solvent solution in the stripper to regenerate the solvent solution. Regenerated solvent solution lean in carbon dioxide SOL4 is recycled back the absorber via the recuperative heat exchanger as stream SOL1. A gas stream that is rich in carbon dioxide is produced in the stripper and may be sent to storage.

With reference to Figure 2, the method includes a multi-objective optimisation algorithm combined with commercially available simulation software, namely AspenPlus™, and an Excel/Visual Basic method to perform pinch analysis on a coal fired power station with carbon dioxide capture and storage (CCS) to determine the maximum amount of power that can be generated by the simulated process by performing a linear programming optimisation. The method is designed to enable the optimisation of the power station and CCS plant variables to enable the designer to select operating variables and process flowsheets that maximise the amount of power generation. The program has been applied to carbon capture based on solvent absorption but can equally be applied to any form of carbon capture technique. The steps 1 to 12 of Figure 2 will now be described in detail. 1. MOO Setup - Problem Definition

One example of a multi-objective optimisation algorithm is a MOO algorithm by G.P. Rangaih of the National University of Singapore. The MOO algorithm used in this example is an Excel/VBA based program, however, other programs and other programming languages could equally be used. The optimisation algorithm is a binary version of the Non-dominated Sorting Genetic Algorithm Version II (NSGAII) created by K. Deb (Indian Institute of Technology Kanpur). The first step of the program is to select the objective/objectives, 8712584_1 (GHMatters) P83932.AU.1 14 the decision variables, constraints and the MOO parameters for the particular study. The NSGAII code works by creating a population of n individuals, each individual has its own values for each of the decision variables. In the first iteration these values can be randomly selected, however for subsequent iterations the selection of these values is biased towards values that provide results that are more favourable to the objective. New generations of individuals are created by combining two individuals, called parents, which display results that are favourable to the objectives. The new individuals can also have random changes, called mutations, made to the values of the variables to enable the individuals to have variations in the values of the decision variables to the parents. Each new generation is compared to the former generations and those individuals that have results that are more favourable to the objective are kept in the population and become the parents of the next generation. This process is continued for m number of generations.

The MOO algorithm requires NSGAII specific parameters to be defined; which include the population size (n), the number of generations (m), the random seed, the selection type, crossover type, crossover probability, mutation type and mutation probability. There are also problem specific parameters that can be defined; the number of objectives and whether those objectives are to be maximised or minimised has to be specified. For each decision variable the range (minimum and maximum) of values needs to be provided along with whether the decision variable is a continuous or discrete (integer) variable. The number of bits for the decision variable can be selected, which sets the interval between each individual possible from within the range for the decision variable. For example a continuous variable with a range of O(min) to 1.5(max) and a bit size (b) of 2 will have intervals of 0.5 (calculated by Equation 1 and therefore that variable could either take any of the following forms 0, 0.5, 1 or 1.5.

Interval Size = (Max-Min) / (2b-1) (Equation 1)

Constraints can also be included in the problem definition, these constraints need to be defined as lesser than or greater than a specified value. The constraint may be one of the objectives such as C02 capture greater than 80% or may be a separate variable altogether, such as the proportion of steam extracted from the turbine.

There will usually be two objectives, including, but not limited to, the amount of C02 captured and the power generated from the power station or the power generated and the capital cost of the plant. The program also handles a single objective or more than two objectives. Examples in this description are based on two objectives; the amount of C02 captured and the power generated by the power station. 8712584J (GHMatters) P83932.AU.1 15

Any number of decision variables may be selected for the particular study which can include but are not limited to the solvent flowrate, lean solvent loading, stripper pressure, stripper rich solvent feed temperature, flue gas feed temperature, absorber lean solvent temperature, absorber height, stripper height, level of coal pre-drying and the number of C02 compression stages. 2. Set up Simulation

The power station and CCS plant are simulated in the process simulation software (AspenPlus®). The simulations need to be designed so that the decision variables are process input specifications so that changes in the decision variables will make the appropriate changes in the simulation. For example, if the lean solvent loading is a decision variable, the simulation needs to have the lean solvent loading as an input and the stripper needs to be designed to ensure the specified lean solvent loading is attained in the stripper bottoms and that the feed to the absorber is equal to the specified lean solvent loading. 3. Set up Stream & Turbine Information

The steam turbine information is input into a specific format in Excel. Each possible steam extraction point from the turbine needs to be provided for the process. This step is used to define both the quality of the steam available for process heating and the amount of electricity that the steam can produce. 4. Set up Heat Integration or Heat Pinch Analysis

The simulation streams that should be included in the heat pinch analysis need to be selected. A VBA program provides all the available processes in the defined simulation and the user selects from that list the processes that represent the hot/cold streams required for pinch analysis.

5. Run MOO

At this stage of the process the MOO program can be run. The MOO program will run steps 7 to 10 for each individual in each generation, therefore n times, before progressing to step 11. Steps 6 to 11 are run m times before the results are provided in Step 12. Therefore the program loops through a total ofmxn times. 6. Assign Values to Decision Variable

The MOO program will assign values to each decision variable for each individual in the generation in question. In the first iteration the values for each decision variable will be 8712584_1 (GHMatters) P83932.AU.1 16 selected using a random number generator to attain a value that is within the range of each variable. In subsequent iterations the values of the decision variables will be generated from the individuals in previous iterations that are more favourable to the objectives using rules established in the NSGAII algorithm 7. Run Simulation

For each individual the decision variables that have been selected by the MOO program are exported using VBA to the process simulation program which in this example is AspenPlus®. The process simulator is used to simulate the power station and the CCS plant with the values of the decision variables that have been supplied by the MOO program for that individual case. 8. Pinch Analysis

Once the process simulation is complete, the stream temperature-enthalpy data for the selected streams are extracted from the process simulator. The temperature-enthalpy data for each stream is then simplified using a VBA based algorithm. The stream data is then compiled into composite curves and grand composite curves using a VBA program to automate the established Problem Table Algorithm.

The composite curves/grand composite curves provide the details on the amount of heat that is either; required to provide sufficient heat for the CCS plant, or available to generate steam. The grand composite curves are used as the basis for the linear programming program detailed in Section 9. 9. Linear Programming Program

The linear programming program is an Excel/VBA based algorithm that calculates the maximum amount of power that can be generated for a given grand composite curve with the given turbine.

There are two sets of linear equations that the linear programming program may use for a power plant and carbon dioxide capture facility.

For existing power station designs; there will usually be a deficit of heat due to the addition of the CCS plant. The additional heat will be provided by extracting steam from the steam turbine. The amount of steam that is extracted from the turbine and the location of that steam affect the amount of power that is generated from the turbine. The linear programming algorithm determines the available thermal energy in each of the extraction points and the amount of electrical energy that is sacrificed by extracting that steam from the turbine. This information can be represented as a linear equation at each temperature level 8712584_1 (GHMatters) P83932.AU.1 17 2011261169 13 Feb 2017 and when all temperature levels above the pinch point are combined the set of linear equations can be solved, in this example the Excel Solver add-in (and assuming a linear model). This program calculates the steam extraction rates that will maximise power generation. 5 By way of example, the linear programming algorithm can be used for retrofit designs where the conditions of the existing steam cycle are already known. The grand composite curve is used to determine the minimum amount of heat required to satisfy the deficit of heat created by the addition of the carbon dioxide capture facility. The problem objective is to determine the extraction steam requirements to satisfy the deficit of heat ίο whilst maximising the amount of power generated from the power station, ie. by minimising the amount of power ‘lost’ by the extraction steam.

The amount of steam extracted at each level is a linear optimisation problem with n number of variables, where n is the number of steam levels not including the last, normally condensing stage. Figure 3 is a graphical representation of steam turbine model having a is number of steam levels available for use in the carbon dioxide capture facility. The last stage is not considered as this stage is set by the lowest cold sink, which is usually cooling water and should not provide any useful heat.

The amount of power lost by extracting steam, between each level i, can be calculated using equation 2, which is the difference in enthalpy for an isentropic expansion 2 0 of the steam to the next level multiplied by the isentropic efficiency of the turbine. wiJ+i = f;. u+i.(hi - hiseni(Pi+1,Si)) (Equation 2)

Where the nomenclature of Equations 2 to 10 is as follows.

Nomenclature Symbols Subscripts h. Enthalpy of the steam at extraction i ith section of the turbine (0 = Steam point i. (kJ/kg) supply, n = hisen.i Enthalpy of the steam at extraction last steam extraction point, n+1 = point i steam outlet of assuming isentropic expansion from turbine) stage i -1. (kJ/kg) I Ith section of the turbine Η,,, Enthalpy available in steam i j The number of temperature intervals between the steam at in the GCC temperatures t and the turbine and the SCC. outlet. If t is greater than the steam supply temperature k Total number of steam extraction then it is the points from the difference from the supply turbine not including the final 8712584_1 (GHMatters) P83932.AU.1 10 (Equation 4) 2011261169 13 Feb 2017 18 temperature down to section. the turbine outlet. (kJ/kg) t tth temperature interval in the combined list of fi Mass Flowrate of the steam exiting the ith section of the turbine, (kg/s) temperatures in the GCC and the SCC (1 = Hottest temperature (Ttop), m = pinch point temperature). Pi Qxs Pressure of the steam exiting the ith section of the turbine. (kPa) The excess energy in the SCC above that required to meet the heat duty (kW) Ttop The hottest temperature in the GCC or SCC. Greek Letters Si Entropy of the steam exiting the ith section of the turbine. (kJ/kg K) i Specific amount of power generated by the turbine from steam at the turbine section i Ti Temperature of the steam exiting the ith section of the turbine. (°C) to the outlet of the turbine (kJ/kg). Isentropic efficiency of the turbine. w Turbine power that could be generated with the Abbreviations steam utilised from all extraction points. (kW) CCS Carbon Capture and Storage wu Work generated from the turbine between two steam GCC Grand composite curve w extraction points i and I. (kW) Turbine power that can be generated from the turbine with the given generation and extraction rates. Qxs The excess energy in the SCC above that required

The total power lost for the steam extraction at each level can, therefore, be calculated by summing up the energy lost in each stage of the turbine downstream of where the steam was extracted (Equation 2). k

WiMl = fi i,i+l (lli - Keni (Pi+1 >Si)) = fi®i i=i (Equation 3)

The total power lost from all of the steam extraction points is the summation of the power lost by the steam extracted at each extraction point (Equation 4). k k k W = Σ fi Ση /,.-+1 (hi - Keni (PM . T )) = Σ /=1 /=/ /=1 8712584_1 (GHMatters) P83932.AU.1 19 2011261169 13 Feb 2017

There are also two constraints; the first is that the extraction steam provides sufficient energy to overcome the deficit of heat required by the process and that this energy is provided at temperatures greater than that required by the process. This can be shown by plotting the steam composite curve (SCC), the composite curve of all the extraction steam, 5 on the same graph as the GCC. These two constraints are met when the deficit of heat shown by the GCC is supplied by the SCC and the SCC lies to the left of the GCC for all temperatures above the pinch point as shown in Figure 4.

When each steam extraction level temperature and pressure is fixed, as they have been in this retrofit case, the amount of energy lost from the turbine and the amount of ίο energy available in the steam are both linear and therefore the problem can be solved by linear programming to minimise the amount of power lost from the turbine (Eq. 5) subject to a series of inequality equations which are provided by the two aforementioned constraints. The only variables in this problem are the mass flowrates of steam extracted at each steam level. k is Objective Minimise = ^/ω, =νν (Equation 5) i=l

Subject to: k Σ7 fy,Ttop ^ GCCTtoP (Equation 6) i= 1 k V t = 2, 3,...j ΣίΑ* ύGCC, +Qxs (Equation 7) i=l k

Where: Qxs=YJfihiTt0p-GCCrtop (Equation 8) i=1

2 o The first constraint (Eq. 6) is to ensure the amount of energy provided by the SCC is greater than the deficit of heat required by the process as indicated by the GCC. The second constraint (Eq. 7) is a series of constraints that ensures that at every temperature from the highest GCC temperature to the pinch point the SCC lies to the left of the GCC, that is, there is sufficient energy in the steam for the process requirements. The term Qxs (Eq. 7 25 and 8) is required so that the SCC starts at the same relative enthalpy as the deficit of heat represented by the GCC and allows for the situation where the optimal amount of steam extracted may be higher than the deficit of heat. 8712584_1 (GHMatters) P83932.AU.1 20 2011261169 13 Feb 2017

The problem can be arranged as a matrix with k columns and j + 1 rows. The first row of the matrix is made up of the coefficients for the specific amount of power lost for each steam level ( ,). The number of rows for the inequality constraints are defined from the number of temperature intervals (j) in the GCC and SCC. The coefficients for the 5 subsequent rows of the matrix are made up of the amount of energy (hijt) in the extraction steam from each temperature interval down to the GCC pinch point. The variable matrix is the quantity of steam extracted at each steam level (f,). The solution matrix includes the right hand sides of equations 5, 6 and 7. ίο Matrix Form: " ®1 ^h.Ttop ω2 ,/top ω* " W.Ttop 7Γ Λ > w GCCTtop h\,2 h22 W, 2 < gcc2 + qxs _ Kj Kj -1 • -¾ /*_ < GCC j + Qxs

This can then be solved using a linear programming method (such as the simplex algorithm) which are included in many mathematical software packages.

For new power station designs; the steam circuit can be constructed to maximise is the power generation with the available heat. The CCS plant will usually diminish the amount of heat but there will still be a surplus of heat. The amount of steam generated and the amount of steam extracted from the turbine is calculated to maximise the power generation. The thermal energy to generate steam and the thermal energy available in the extraction steam is calculated as well as the amount of power that can be generated for the steam 2 0 generated or the amount that is lost from the extraction steam. This information is put into a linear equation at each temperature interval, all temperature intervals combined produce a set of linear equations which can be solved to determine the amount of steam generated and extracted from the turbine to maximise the power generated from the available heat.

In the case of a new plant and carbon dioxide capture facilities, the linear 25 programming algorithm is analogous to the linear programming algorithm described above except that rather than trying to determine what the optimum extraction steam rates are to minimise the amount of power ‘lost’ from the turbine for a given deficit of heat, the optimum rates of steam generation and extraction are calculated to maximise the amount of power generated with the available heat in the process. The available heat in the process is 8712584_1 (GHMatters) P83932.AU.1 21 2011261169 13 Feb 2017 represented by a GCC and a SCC is generated that lies under the GCC as shown by Figure 5.

The aim is to calculate the amount of steam generated (F) or used (f) at each steam level to maximise the amount of power generated (W) (Eq. 9). This is subject to the 5 constraint that there must be sufficient heat at each temperature level to satisfy the requirements of the SCC. That is, the SCC must be less than the GCC at all temperatures as per Equation 10. ,

Objective Maximise = ^(/-/)(0,=^ (Equation 9) i= 1 ίο Subject to V t = 1 ...j YjkFiHit -///< GCCt (Equation 10) i=l

These equations can also be represented in matrix form and solved using linear programming. Set out below are linear equations for a steam turbine arrangement with 4 steam levels. w #2 < GCCX 1 2 3 4 1 2 3 4 #3 < gcc2 #,., #2,1 #3,1 #4,1 #1,1 #2,1 ^3,1 ^4,1 #4 < j j • • • / < #u #2,, #3,, #4,, Kk ^2,, ^3,, ^4., _ Λ < /3 < Ja_ < GCCk_ 15

It should also be noted that it is possible to add additional constraints; such as maximum main steam flowrate limitations etc. The linear optimisation algorithm works assuming that the pressure of the extraction steam is known, and therefore needs to be assumed in a new build steam cycle. Flowever, with the multi-objective optimisation the 2 0 steam pressures may also be a variable which enables the optimisation of the steam pressure for the process under review. 10. Calculate Objectives

The results from the linear programming program for the amount of power 25 generated by the power station combined with results from the simulation as to the electrical 8712584J (GHMatters) P83932.AU.1 22 demand of the power station and CCS plant are combined to calculate the net power from the power station. Other objectives such as the amount of C02 captured or capital costs can be calculated based on results from the simulation and the linear programming program results. The calculated objectives are returned to the MOO program. 11. Objective Comparison

The MOO stores the objective values for each individual and after the objective values for the entire population are calculated the results are compared to the best results from previous iterations. The n individuals that have the best results with relation to the objectives, the Pareto optimal solutions, will remain in the solution set.

The n individuals that remain in the solution set become the parent individuals for subsequent generations, and therefore the values of each of the decision variables for each individual will be based on these parent individuals. The selection of these variables occurs in Step 6. 12. Results

After m number of generations the final n best individuals is the solution set. The results provide a set of solutions that are the Pareto optimal solutions for the m χ n individuals that were tested in running the program. The solution set can be used to examine what decision variables are likely to provide the best results with regard to the objectives.

TEST EXAMPLES AND RESULTS

The program described above in relation to Figure 2 has been tested on two examples comprising a coal fired power station and a potassium carbonate solvent system for capturing carbon dioxide.

Example one

Example one simulates a power station having a sub-critical unit with a nominal capacity of 200MW. The carbon dioxide capture plant is added to the outlet of the existing power station to capture the C02 which is compressed to 100bar. A total of four cases were tested. Cases 1 and 2 consider the variables of solvent loading and flowrate, and stripper pressure in order to optimise the reboiler energy. Cases 3 and 4 consider the optimisation of the net power output of the power station rather than just the reboiler energy requirements. Details of the cases and results of the tests are as follows.

Case 1 a/b: Solvent loading and flowrate

For this case the flue gas from the power station unit is added directly to the solvent 8712584_1 (GHMatters) P83932.AU.1 23 2011261169 13 Feb 2017 plant at 40°C, the lean solvent enters the absorber at 65°C and the stripper pressure is fixed at 1.5Bara. The column heights are also fixed at 20m and 15m for the absorber and stripper respectively. The columns are modelled using the Aspen Plus™ Rate Based RadFrac column. The range for each of the variables for this case and the others are shown in Table 5 1. The objectives for this case are maximising the amount of C02 captured and minimising the reboiler energy.

Table 1. Variable range and objectives

Case Solvent flow kg/s Solvent lean loading mol Stripper pressure Objective. 1 Objective .2 C02/molK2C03 (Bara) 1a 2200-2300 0.21-0.23 1.5 C02 Capture (% C02) Reboiler Energy (MJ/kg) 1b 2000-3260 0.175-0.33 1.5 C02 Capture (% C02) Reboiler Energy (MJ/kg) 2 1000-4150 0.1-0.4 0.3-3.3 C02 Capture (% C02) Reboiler Energy (MJ/kg) 3 1000-4150 0.1-0.4 0.3-3.3 C02 Capture (% C02) Power station net power (MW) 4 1000-4150 0.1-0.4 0.3-3.3 C02 Capture (% C02) Power station net power (MW) ίο Case 2: Solvent loading, flowrate and stripper pressure

This case is an extension of the first case however it includes a third variable; the stripper pressure. The rest of the power station unit and solvent plant are kept constant like the first case. The variable ranges have also been increased; which are shown in Table 1. is Case 3: Power station unit’s net power output

The third case uses the same three variables and the same ranges, but rather than minimise the reboiler energy, the optimisation is to maximise the power station unit’s net power output. The unit’s net power is reduced by the addition of the CCS plant. The flue gas pressure is increased by the use of a fan, the solvent is circulated by pumps and the C02 2 0 compressors all require power. The heat for the solvent reboiler is supplied from steam extracted from the steam turbine which leads to a reduction in the power produced by the power station unit. In this case, the steam extraction is from an existing bleed point on the exhaust of the high-pressure turbine (5.6bar /177°C) and the amount of steam that needs to be extracted from the turbine is calculated based on the reboiler energy demands. For this 8712584J (GHMatters) P83932.AU.1 24 paper it is assumed that the turbine efficiency is not affected by the reduction in steam flow from the turbine. The net power produced from the power station unit is therefore calculated by the amount of power produced by the turbine minus the existing power loads and the new power loads caused by the addition of CCS.

Case 4: Power station unit’s net power output with heat integration

When CCS is added to the power station unit there are a number of waste heat sources that are also added; the C02 compressors, the stripper condenser and flue gas which should be cooled down prior to the solvent plant. These waste heat sources may be able to be utilised elsewhere in the power station and the CCS plant to reduce the amount of steam that needs to be extracted from the turbine and increase the power produced from the turbine.

For this case, after the simulation has solved in Aspen Plus™ the stream data for all the hot and cold streams are automatically extracted from the simulation and processed using the pinch analysis problem table algorithm. This calculates the deficit of heat in the given process. The amount of steam extracted from the turbine is then calculated using a linear programming program. These results are then used to calculate the net power output from the power station unit and returned to the optimisation program as the objective.

Results of Case 1a/b: Solvent loading and flowrate.

In this example two different ranges have been used for the two decision variables; a tight range with solvent lean loading of 0.21-0.23molC02/molK2C03(s) and 2200-2300kg/s of lean solvent and a wider range with lean loading of 0.2-0.3molC02/molK2C03(s) and 2000-3000kg/s, the Pareto-optimal solutions for these cases are shown together in Fig 6.

When the tighter range was used, as expected the range of C02 captured is reduced, but the reboiler energy for the same amount of C02 captured was increased, compared to when a wider range of flowrates and loading were used. Most of the tight range results were dominated by the solutions from the wider range case (1b), which means that most of the solutions for the wider range were better than those for the tight range. This demonstrates an advantage of the multi-optimisation approach, where the input parameters may be varied over very wide ranges.

There is a near-linear relationship between the reboiler energy for the Pareto-optimised solutions and the lean solvent loading (refer to Fig 7). Flowever for the wider range, the optimal solution for higher reboiler energy and hence higher capture rate are approaching the lower limit of the lean solvent loading provided (0.175molCO2/molK2CO3(s)). 8712584_1 (GHMatters) P83932.AU.1 25

An explanation for the solutions from the wider range case being superior to the tighter case is that the solvent flowrate, especially for the lower loadings is limited by the range of solvent flowrates as the Pareto-optimal solutions are all tending towards the upper bounds of 2300kg/s as shown in Fig 8. Therefore, to optimise the system for both the amount of C02 captured and reboiler energy, flowrates higher than 2300kg/s are required for solvent loadings between 0.21 - 0.22molCO2/molK2CO3(s).

Results of Case 2: Impact of Stripper Pressure

The previous examples all maintained a constant stripper pressure of 1.5bara, whereas the following cases look at the impact of varying the pressure on the reboiler energy. As discussed in the introduction, a lower pressure is thought to reduce the reboiler energy for a carbonate system. This is confirmed in Fig 9 where the variable pressure solutions are better than the fixed pressure solutions and in Fig 10 where all the optimised variable pressure is at 0.3bar; the lowest possible pressure allowed in the range.

The optimal solutions again have solvent loading as nearly linear with the reboiler energy until the reboiler energy reaches 6MJ/kgC02 after which the solvent regeneration becomes increasingly difficult.

Results of Case 3: Impact of variables on the power station unit’s net power

This case looks at optimising the power station unit’s net power output rather than the reboiler energy by varying the solvent loading, flowrate and stripper pressure. The results are shown in Fig. 11 for both Case 3 and Case 4 which will be presented in the next section. Fig. 11 shows that as the capture rate of C02 increases the net power produced from the unit decreases.

For Case 3, the stripper pressure (when the overall net power from the power station unit is considered) do not all tend to 0.3bara. The pressure is more scattered and is tending towards 0.7-0.9bara rather than 0.3bara. The optimised solutions for the solvent loadings for Cases 2 and 3 are very similar for the C02 capture rate, see Fig 12.

Results of Case 4: Impact of variables on the power station net power with heat integration The final case looks at the impact of the three variables on the overall output of the power station when heat recovery is maximised. The Pareto-optimal solutions are shown for the net power produced by the unit versus the capture rate in Fig. 13. These points are all dominant over Case 3, which does not consider heat integration of the CCS plant with the power station. The power station unit’s output between the heat integrated and non-integrated case is between 20-30MW over the range of capture rates. The maximum capture 8712584_1 (GHMatters) P83932.AU.1 26 rate of C02 is also greater for Case 4 compared to Case 3 (refer to Fig 13). Case 3 is limited to 90% capture of C02 as the steam demand for any further capture exceeds the amount of steam available from the turbine of the power station unit.

The optimised points for Case 4 show that low stripper pressures are not necessarily preferred when the overall power plant is taken into consideration. As shown in Fig 13, the stripper pressure tends to be between 1,7-2.5bara compared to around 0.7bara for the case without heat integration (Case 3).

It is also interesting to note that the solvent lean loading for the heat integrated case is quite different to the others as shown in Fig 14. Cases 2 and 3 appear to have a reasonably uniform relationship between the capture rate of C02 and the lean solvent loading. In contrast with Case 4 the optimum lean loading of the solvent is 0.26molCO2/molK2CO3, for capture rates between 40-80%.

Example two

Example two shows use of the program to optimise the power station retrofitted with potassium carbonate based C02 capture with respect to both the energy aspects and the project economics. This example uses a 500MW power station and apart from the increase in plant size, it is analogous to the power station in Example one, except the steam cycle is more complex. The steam cycle has a single stage of reheat and high pressure boiler feed water heaters. Flowever, the program works in the same manner, calculating the maximum power that can be generated for the given steam cycle for a given set of operating parameters.

The optimisation involves estimation of the differential cost of electricity, which is achieved by extracting design information from the simulation and the heat integration problem (the heat exchanger costs) to estimate the new capital and operating costs of the power station attributed to the CCS plant.

This example optimises nine variables including the solvent lean loading and flowrate, the feed gas, solvent and regenerator feed temperatures, the absorber and regenerator packing height, the regenerator pressure and the heat exchanger network minimum approach temperatures. Two multi-objective optimisation cases are performed, in both cases the first objective is to maximise the amount of C02 captured, and in the first case the second objective is to maximise the net power produced from the power station, whilst the second case the second objective is to minimise the differential cost of electricity.

Select results from the program are provided in Figures 15-18. Figure 15 shows the maximum net power that can be produced from the power station for given capture rates for both optimisation cases. Of interest, is that for this example, the maximum amount of power 8712584J (GHMatters) P83932.AU.1 27 2011261169 13 Feb 2017 that can be produced from the power station is approximately 10% greater than the amount of power that would be produced when trying to minimise the differential cost of electricity. This example enables the designer to investigate the trade-off between capital and operating costs and as a result it appears that the differential cost of electricity can be reduced by up 5 to 15 $/Mwh by optimising the plant to minimise the differential cost of electricity rather than necessarily producing the maximum amount of power from the power station.

Using the results from the optimisation case studies in this example, it is possible to determine the anticipated capital and operating costs, as well as the optimum operating parameters of the solvent capture plant. The capital costs for both optimisation cases have ίο been provided in Figure 17. This graph shows that the capital costs involved to maximise the power station net power are 200 - 300% that to minimise the differential cost of electricity and helps to explain why producing the maximum amount of power may not result in the cheapest price for electricity in the example provided. As well as the overall capital costs it is possible to break down the capital costs to determine how they change with varying capture is rates and/or what the major capital cost items might be.

In Figure 17 the optimal solvent flowrate is shown for the optimisation to minimise the differential cost of electricity. These curves would be useful in the operation of the solvent plant to control the capture rate, where control of the capture rate may be important to maximise power station profits. Similar curves can be generated for many variables 2 0 including the solvent lean loading, operating temperatures and regenerator pressures.

It will be understood to persons skilled in the art of the invention that many modifications may be made without departing from the spirit and scope of the invention.

In the claims which follow and in the preceding description of the invention, except where the context requires otherwise due to express language or necessary implication, the 25 word “comprise” or variations such as “comprises” or “comprising” is used in an inclusive sense, i.e. to specify the presence of the stated features but not to preclude the presence or addition of further features in various embodiments of the invention. 8712584J (GHMatters) P83932.AU.1

Claims

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:

1. A method of optimising a power plant combusting fuels to raise steam to generate power and a carbon dioxide capture facility which captures carbon dioxide from the power plant using a multi-objective optimisation algorithm, the method comprising: a) selecting one or more variables relating to the plant and the carbon dioxide capture facility, each variable comprising a range of values, wherein the variables selected for the power plant are temperature and pressure of the steam raised by the power plant, and the variables of the carbon dioxide capture facility is an amount of energy utilised by the carbon dioxide capture facility; b) applying the multi-objective optimisation algorithm to determine a population of individuals, where each individual includes a set of values for each variable within respective ranges of values; c) determining operating conditions of the plant and the carbon dioxide capture facility by conducting process and heat integration analysis on selected streams of the power plant and the carbon dioxide capture facility by comparing differentials in energy supply and energy demands over temperature levels based on the determined sets of values of the individuals and calculating a selected objective which includes a minimum of the amount of energy utilised by the carbon dioxide capture facility and thereby taken from the power plant according to the following equations

(5)

and subject to the (6)

(7) wherein k Number of steam extraction points j Number of temperature intervals f. Mass flowrate of the steam exiting the ith section of the turbine (kg/s) □i Specific amount of power generated by the turbine from steam at the turbine section i to the outlet of the turbine (kJ/kg) w Turbine power that could be generated with the steam utilised from all extraction points (kW) hijt Enthalpy available in steam i between the steam at temperatures t and the turbine outlet, if t is greater than the steam supply temperature then it is the difference from the supply temperature down to the turbine outlet (kJ/kg) t the temperature interval in the combined list of temperatures in the GCC and the SCC (1 = Hottest temperature (Ttop), m = pinch point temperature) Ttop The hottest temperature in the GCC or SCC GCCt Energy in the grand composite curve at temperature t Qxs The excess energy in the SCC above that required to meet the heat duty (kW) d) comparing and outputting the minimum of the amount of energy utilised by the carbon dioxide capture facility determined in step c) and thereby taken from the power plant; and e) configuring the plant and the carbon dioxide capture facility so as to operate in accordance with the operating conditions determined in step c).
2. The method according to claim 1, wherein the optimised objective has been obtained when no further improvement of the objectives can be obtained.
3. The method according to any one of claims 1 to 2, wherein the variables selected in step a) also include any one or a combination of the following: • variables that effect operating conditions of the plant; • variables that effect operating conditions of the carbon dioxide capture facility; • variables that are a function of capital cost of the plant; • variables that are a function of capital cost of the carbon dioxide capture facility.
4. The method according to any one of claims 1 to 3, wherein step a) includes selecting multiple variables, i.e., x number of variables and a population size of multiple individuals , i.e., n individuals, and steps b) and c) are performed n number of times whereby separate sets of values for each variable within respective ranges of values are determined, and in turn, a respective objective is determined.
5. The method according to any one of claims 1 to 4, wherein the method is iterative whereby the objectives determined in step c) are compared in step d) with the determined objectives of previous iterations, and based on the comparison, the method includes repeating steps b) to d) a predetermined number of times or until a difference between the objectives of consecutive iterations is minimised or within an acceptable deviation margin.
6. The method according to claim 5, wherein the method compares the objectives for each individual determined by one of the iterations, with the best results of objectives determined in previous iterations to determine the optimised objectives.
7. The method according to claim 5 or 6, in which when the objectives are outside the acceptable margin, the steps b) to d) are repeated using the population set of values having a corresponding objective that is the closest to the optimised objective.
8. The method according to any one of claims 5 to 7, wherein each iteration of determined objectives is compared with previous iterations and those iterations determined to be closer to the optimised objective replace the previous iterations for subsequent comparison.
9. The method according to any one of claims 5 to 8, in which steps b) to d) are being repeated in a subsequent iteration, the multi-objective optimisation algorithm regenerates a revised population set of values for the variables.
10. The method according to any one of claims 5 to 9, wherein the revised population set of values are generated by the multi-objective optimisation algorithm that favours the objectives based on previously determined objectives.
11. The method according to any one of claims 1 to 10, wherein step c) includes conducting heat pinch analysis on selected streams of the plant and the carbon dioxide capture facility to provide a grand composite curve that identifies either one or a combination: i) energy sources within the plant and carbon dioxide capture plant; and ii) energy demands to run the plant and carbon dioxide capture plant.
12. The method according to claim 11, wherein pinch analysis includes: i) creating a profile of the sum of the energy of the selected hot streams of the power plant and selected hot stream of the carbon capture facility; ii) creating a profile of the energy of selected cold streams of the power plant and selected cold stream of the carbon dioxide capture facility (i.e., composite curves); and iii) creating from the profiles created in i) and ii) a grand composite curve showing an amount of the surplus or shortfall in heat.
13. The method according to any one of claims 1 to 12, wherein step c) includes applying the linear programming algorithm to maximise an amount of power that can be generated by the power plant for a given composite curve determined by the pinch analysis.
14. The method according to claim 13, wherein the power plant and the carbon dioxide capture facility include an energy source having known amounts of energy over given temperature levels, and the linear programming algorithm can minimise the amount of energy utilised by the carbon dioxide capture facility and thereby taken from the plant as a function of the available energy at each temperature level.
15. The method according to claim 14, wherein the power plant and the carbon dioxide capture facility include an energy source having an unknown amounts of energy, and the linear programming algorithm can maximise the amount of power generated by the power plant as a function of the amount of energy available and the amount of energy used by the carbon dioxide capture facility.
16. The method according to any one of claims 1 to 15, wherein the carbon dioxide capture facility is characterised as being either one or a combination of solvent absorption, membrane separation, physical and chemical adsorbents, low temperature hydrates.
17. The method according to any one of claims 1 to 16, wherein the carbon dioxide is removed using pre-combustion capture, post combustion capture or an oxyfuel process.
18. The method according to any one of claims 1 to 17, wherein the amount of steam at temperature and pressure levels of the plant for generating power is maximised according to the following equations

(9) and subject to:

(10) wherein F, Mass Flowrate of the steam generated in the ith section of the turbine(kg/s) k Number of steam levels j The number of temperature intervals in the GCC and the SCC f. Mass flowrate of the steam extracted from the ith section of the turbine □, Specific amount of power generated by the turbine from steam at the turbine section i to the outlet of the turbine (kJ/kg) W Turbine power that could be generated with the given steam generation and utilisation rates(kW) Flijt Enthalpy of steam generated in steam level i at a temperature half the minimum temperature difference above the actual temperature (kJ/kg) hijt Enthalpy of the steam at extraction point i at a temperature half the minimum temperature difference below the actual temperature. (kJ/kg) GCCt Energy in the grand composite curve at a temperature t.