Modeling, Simulation and Optimization of Energy Systems using Aspen Plus Giovanni Manente University of Padova University of Ljubljana, April 2017
Outline of the presentation Flowsheet simulation 3 Sequential modular vs Equation oriented modeling 7 Structure of a simulation program 9 Fluid properties 12 Unit operation models 18 Sensitivity analysis, design specifications, calculator blocks 24 Flowsheet convergence 31 Modeling, simulation and optimization of a gas turbine 43 Modeling, simulation and optimization of an ORC system 65 Advantages/disadvantages using Aspen Plus in the energy field 82 Appendix: Enthalpy calculation 85 2
Process Flowsheet The process flowsheet, also known as the process flow diagram (PFD) is the key document in process design It shows the arrangement of the equipment selected to carry out the process; the stream connections; stream flow rates and compositions; and the operating conditions. A block diagram is the simplest form of flow diagram. Each block can represent a single piece of equipment or a complete stage in the process Use of process simulation tools to generate the heat and material balances for the flowsheet 3
Aspen Plus V9 User interface 4
Flowsheet Simulation What is flowsheet simulation? Use of a computer program to quantitatively model the characteristic equations of a chemical process or an energy system Uses underlying physical relationships: Mass and energy balance Equilibrium relationships Rate correlations (reaction and mass/heat transfer) Predicts Stream flowrates, compositions, and properties Operating conditions 5
Advantages of Simulation Reduces plant design time Allows designer to quickly test various plant configurations Help improve current process: Answer «what if» questions Determines optimal process conditions within given constraints 6
Approaches to Flowsheet Simulation Sequential Modular (SM) Each unit operation block is solved in a certain sequence Equation Oriented (EO) All equations are solved simultaneously 7
Equation Oriented versus Sequential Modular (EO vs SM) Sequential Modular (SM) is the standard modeling approach in Aspen Plus Solves each block in the flowsheet in sequence, where given its inlet streams, each block computes its outlet streams When recycles are present, flowsheet iteration is required Although effective for many types of simulations, it can be very time-consuming for certain types of problems Equation Oriented (EO) modeling is an alternate strategy for solving flowsheet simulations Instead of solving each block in sequence, EO gathers all the model equations together and solves them at the same time (AspenTech Training Manual) 8
Structure of a typical simulation program (1) 1. A main executive program that controls and keep track of the flowsheet calculations and the flow of information to and from the subroutines 2. A library of equipment performance subroutines that simulate the equipment and enable the output streams to be calculated from information on the inlet streams (Chemical Engineering Design, Elsevier, 2013) 9
Structure of a typical simulation program (2) 3. A data bank of physical properties 4. Subroutines for thermodynamics 5. Subprograms and data banks for equipment sizing and costing 10
Structure of a typical simulation program (3) In a sequential-modular program, the executive program sets up the flowsheet sequence, identifies the recycle loops, and controls the unit operation calculations, while interacting with the unit operations library, physical property databank and the other subroutines. The executive program also contains procedures for the optimum ordering of the calculations and routines to promote convergence. 11
Specification of Components and Selection of physical property models The first step in building a process simulation is establishing the chemical basis for the model This consists of: 1. Choosing the components (fluids or solids) that will be included in the process 2. Deciding which models to use for the prediction of thermophysical properties These selections are made in Aspen Properties Environment 12
Using Equations of State An essential ingredient for the calculation of properties such as the specific internal energy, enthalpy, and entropy of a substance is an accurate representation of the relationship among pressure, specific volume, and temperature The p-v-t relationship can be expressed using analytical formulations called «equations of state» (EOS) The ideal gas equation of state (pv=rt) provides an acceptable approximation at many states, including but not limited to states where the pressure is low relative to the critical pressure and/or the temperature is high relative to the critical temperature of the substance under consideration. At many other states, however, the ideal gas EOS provides a poor approximation 13
Using Equations of State Over 100 equations of state have been developed in an attempt to improve on the ideal gas equation of state In general these equations exhibit little in the way of fundamental physical significance and are mainly empirical in character Most are developed for gases, but some describe the p-v-t behavior of the liquid phase Every equation of state is restricted to particular states. This realm of applicability is often indicated by giving an interval of pressure where the equation can be expected to represent the p-v-t behavior faithfully 14
Two-Constant Equations of State Van der Walls equation of state: Redlich-Kwong equation of state: 15
Equations of State Features and limitations of the most commonly used EOS: (Chemical Engineering Design, Elsevier, 2013) 16
REFPROP model REFPROP is an acronym for REFerence fluid PROPerties. This model, developed by the National Institute of Standards and Technology (NIST), provides thermodynamic and transport properties of industrially important fluids and their mixtures with an emphasis on refrigerants and hydrocarbons, especially natural gas systems. The REFPROP model uses the most accurate equations of state and models currently available The REFPROP model is designed to provide the most accurate thermophysical properties currently available for pure fluids and their mixtures 17
Simulation of Unit Operations In Aspen Simulation Environment the process simulation is built up by using a set of unit operation models connected by mass and energy streams These operations can be selected from a palette or menu and then connected together using the simulator graphical user interface 18
Unit Operation Model Types Unit Operation Models available in Aspen Plus: Mixer/Splitters Separators Heat Exchangers Columns Reactors Pressure Changers Manipulators Solids User Models 19
Heat Exchangers The Heater block produces a single outlet stream at a specified thermodynamic state. A Heater can be used to represent: heaters, coolers, valves ecc. The HeatX is used to represent a Two-stream heat exchanger. Use HeatX when both the cold and hot sides are important. (AspenTech Training Manual) 20
Pressure Changers The Pump block can be used to simulate: Pumps, Hydraulic turbines The Compr block can be used to simulate: Compressors, Turbines Work streams can be specified to directly obtain the power absorbed or generated (AspenTech Training Manual) 21
Reactors A stoichiometric reactor (RStoic) requires a reaction stoichiometry and an extent of reaction. An equilibrium reactor (REquil) finds the equilibrium product distribution for a specified set of stoichiometric reactions. The Gibbs reactor (RGibbs) solves the full reaction and phase equilibrium of all species in the component list by minimization of the Gibbs free energy. (AspenTech Training Manual) Kinetics Based 22
How to store a Simulation A Backup file contains simulation input and results and requires low disk space. A Backup file is an ASCII file therefore it is transferable between operating systems and it is upwardly compatible 23
Sensitivity Analysis, Design Specifications, Calculator Blocks
Accessing Variables An accessed variable is a reference to a particular flowsheet quantity, e.g. temperature of a stream or duty of a block Accessed variables can be input, results or both The concept of accessing variables is used in sensitivity analyses, design specifications, calculator blocks, optimization etc. 25
Sensitivity Analysis Allow user to study the effect of changes in input variables on process outputs Changes made to a flowsheet input quantity in a sensitivity block do not affect the simulation; the sensitivity study is run independently of the base case simulation Located in Home Analysis Sensitivity (or in Navigation Pane Model Analysis Tools Sensitivity) Results can be viewed by looking at the Results form in the folder for the Sensitivity block Plot results to easily visualize relationships between different variables 26
Uses of Sensitivity Analysis Studying the effect of changes in input variables on process (model) outputs Graphically representing the effects of input variables Verifying that a solution to a design specification is feasible Rudimentary optimization Studying time varying variables using a quasi-steady-state approach Doing case studies 27
Design Specifications Similar to a feedback controller Allows user to set the value of a calculated flowsheet quantity to a particular value Objective is achieved by manipulating a specified input variable Located under Navigation Pane Flowsheeting Options Design Specs Design specifications change the base case, and so results are shown in the core simulation results 28
Design Specifications The calculations performed by a design specification are iterative; providing a good estimate for the manipulated variable will help the design specification converge in fewer iterations The results of a design specification can be found under Navigation Pane Results Summary Convergence DesignSpec Summary; alternatively the final values of the manipulated variables can be viewed directly on the appropriate Stream or Block Results forms 29
Calculator Blocks Allow the user to write equations in a Microsoft Excel spreadsheet or in Fortran syntax to be executed by Aspen Plus Located under Navigation Pane Flowsheeting Options Calculator Results can be viewed by looking at the Results form in the folder for the Calculator block Also, since Calculator blocks change the base case, the core simulation results reflect the influence of the Calculator block The main use of a Calculator Block is to express a function in terms of flowsheet variables Simple Fortran can be translated by Aspen Plus and does not need to be compiled 30
Flowsheet convergence
Tearing the Flowsheet For a sequential-modular simulation program to be able to solve a flowsheet with a recycle, the design engineer needs to provide an initial estimate of a stream somewhere in the recycle loop. This is known as a «tear» stream, as the loop is «torn» at that point The program can then solve and update the tear stream values with a new estimate The procedure is repeated until the difference between values at each iteration becomes less than a specified tolerance, at which point the flowsheet is said to be converged to a solution 32
Tear Stream To determine the tear streams chosen by Aspen Plus, look under the Flowsheet Analysis section in the Control Panel User-determined tear streams can be specified on the Convergence Tear form Providing estimates for tear streams can facilitate or speed up flowsheet convergence (highly recommended, otherwise the default is zero) If you enter information for a stream that is in a «loop» Aspen Plus will automatically try to choose that stream to be a tear stream 33
Convergence Block Algorithms Aspen Plus uses different convergence block algorithms for different functions: To converge tear streams: WEGSTEIN DIRECT BROYDEN NEWTON To converge design specs and tear streams: BROYDEN NEWTON To converge design specs: SECANT BROYDEN NEWTON For optimization: SQP COMPLEX Make changes to global convergence options on the form: Convergence Conv Options Default Methods 34
Convergence Methods Direct Substitution Direct Substitution: In this method an initial estimate, x k, is used to calculate a new value of the parameter, f(x k ). The estimate is then updated using the calculated value: This method is simple to code, but is computationally inefficient and convergence is not guaranteed 35
Convergence Methods Bounded Wegstein (1) The Wegstein method initially starts out with a direct substitution step: An acceleration parameter, q, can then be calculated: where And the next iteration is then: (Chemical Engineering Design, Elsevier, 2013) 36
Convergence Methods Bounded Wegstein (2) If q=0, the method is the same as successive substitution. If 0<q<1, then convergence is damped, and the closer q is to 1.0, the slower convergence becomes If q<0, then the convergence is accelerated. The bounded Wegstein method sets bound on q, usually keeping it in the range -5<q<0 The bounded Wegstein method is usually fast and robust If convergence is slow, then the designer should consider reducing the bounds on q If convergence oscillates, then consider damping the convergence by setting bounds such that 0<q<1 37
Convergence Methods Newton and Quasi-Newton Methods (1) The Newton method uses an estimate of the gradient at each step to calculate the next iteration In the Newton method the value of x at step k+1 is calculated from the value of x at step k using: And the procedure is repeated until (x k+1 -x k ) is less than a convergence criterion or tolerance, e Quasi-Newton methods such as Broyden s method use secants rather than gradients 38
Convergence Methods Newton and Quasi-Newton Methods (2) Newton and quasi-newton methods are used for more difficult convergence problems, for example, when there are many recycle streams, or many recycles that include operations that must be converged at each iteration The Newton and quasi-newton methods are also often used when there are many recycles and control blocks The Newton method should not normally be used unless the other methods have failed, as it is more computationally intensive and can be slower to converge for simple problems 39
Convergence Blocks Every design specification and tear stream has an associated convergence block Convergence blocks determine how guesses for a tear stream or design specification manipulated variable are updated from iteration to iteration Aspen Plus-defined convergence block names begin with the character «$» User convergence blocks can also be specified 40
Flowsheet Sequence To determine the flowsheet sequence calculated by Aspen Plus, look under the «Flowsheet Analysis» section in the Control Panel or on the left pane of the Control Panel window under «Calculation Sequence» User-determined sequences can be specified on the Convergence Sequence form 41
Convergence Problems If a flowsheet is not converged, or if the process simulation software runs and gives a statement «converged with errors», then the results cannot be used for design The designer must take steps to improve the simulation so that a converged solution can be found. The first steps that an experienced designer would usually take would be: 1. Make sure that the specifications are feasible 2. Try increasing the number of iterations 3. Try a different convergence algorithm 4. Try to find a better initial estimate 5. Try a different tear stream 42
Gas turbine: modeling, simulation and optimization using Aspen Plus
Components All components (fluids) appearing in the simulation model are selected: Air is composed of nitrogen, oxygen, argon and CO 2 The fuel is methane The combustion products are CO 2 and H 2 O 44
Methods The ideal gas model is used: pv RT u u(t ) h h( T ) u( T ) RT This is a commonly used assumption when dealing with gas turbine cycles 45
Property Sets A property set is a collection of thermodynamic, transport, and other properties that you can use in physical property tables and analysis In the gas turbine cycle the lower heating value (LHV) is needed to calculate the fuel input and, in turn, the thermal efficiency 46
Simulation environment The required property inputs are complete So, we can move to the simulation environment Here, the first step is building the block diagram of the process/plant (i.e., the gas turbine cycle) 47
Block diagram of the gas turbine cycle The block diagram is built The blocks compressor (COMPR) and turbine (TURB) are taken from the pressure changers library The block combustor (CC) is taken from the reactors library The blocks are linked together by material streams 48
Streams: entering inputs Mass flow rate, temperature, pressure and composition of the stream 1 (air) entering the compressor Mass flow rate, temperature, pressure and composition of the stream FUEL (methane) entering the combustor 49
Blocks: entering inputs (1) Compressor: discharge pressure and isentropic efficiency Turbine: discharge pressure and isentropic efficiency 50
Blocks: entering inputs (2) Combustor: reaction and fractional conversion Complete combustion of methane: balanced chemical equation: CH 4 2O2 CO2 2H 2O In the dialog box the stoichiometric coefficients of the reactants are entered as negative numbers 51
Running the simulation model The model is run (button ) The progress of calculation is shown in the Control Panel In particular the sequence used by Aspen Plus to solve the flowsheet: COMPR CC TURB The simulation generated no errors as shown by Results Available at the bottom of the window 52
Material stream results The simulation results can be seen in the folder Results Summary Streams The window shows the thermodynamic parameters for all the streams in the flowsheet If the results of only one stream are to be investigated: double click the material stream using the right button of the mouse results 53
Block results Double click the block using the right button of the mouse results Compressor Combustor 54
Work stream results Power absorbed by the compressor WCOMPR= 32215 kw Power generated by the turbine (mind the minus sign in the dialog box) WTURB= 67333 kw 55
Calculator block to calculate net power and thermal efficiency Flowsheeting options calculator Definition of the variables Fortran code 56
Results of calculator block The net power is WNET= 35118 kw The thermal efficiency is THEFF= 0,3509 57
Design specification to set the turbine inlet temperature A design specification is defined which varies the fuel mass flow rate to guarantee a turbine inlet temperature equal to 1300 C The variables are defined The turbine inlet temperature (variable name TIT) is specified equal to 1300 C (1573 K) 58
Varied variable in the design specification and results The varied variable is the fuel (methane) mass flow rate which is varied within a given range of variation The results show that the fuel mass flow rate resulting in the desired TIT is 2.499 kg/s 59
Sensitivity analysis to evaluate the variation of performance with pressure ratio Varied variable: compressor discharge pressure Analyzed variables: net power output and thermal efficiency 60
Net power output (kw) Thermal efficiency Results of the sensitivity analysis 50000 45000 40000 35000 30000 25000 20000 15000 10000 5000 0 0,50 0,45 0,40 0,35 net power 0,30 thermal efficiency 0,25 0,20 0 10 20 30 40 50 60 70 Pressure ratio It can be easily seen from the results that the maximum net power output is achieved at a compressor discharge pressure around 16 bar but which is the exact value? 61
Optimization of net power output: problem definition (1) Definition of the variables involved in the optimization problem Definition of the objective function: net power output (variable name WNET) 62
Optimization of net power output: problem definition (2) Definition of the «decision variables» (i.e, variables that are optimized) in the optimization problem The only decision variable in this problem is the pressure ratio of the compressor 63
Optimization of net power output: results (WNET) max = 45466,5 kw (r p ) opt =16,6 bar 64
Organic Rankine cycle: modeling, simulation and optimization using Aspen Plus
Components All components (fluids) appearing in the simulation model are selected: Water: a simple modeling for the geofluid Isobutane: the working fluid operating in the ORC system Nitrogen and oxygen: the main air constituents 66
Property Refprop is used as the property method to evaluate the thermodynamic and thermophysical properties of the working fluid This is chosen as the baseline property method 67
Property sets The dew point temperature is obtained from the property sets library 68
Block diagram of the organic Rankine cycle The block diagram is built The blocks preheater (PREH), vaporizer (VAP) and air cooled condenser (ACC) are taken from the exchangers library The blocks pump (FP) and turbine (TURB) are taken from the pressure changers library The blocks are linked together by material streams 69
Streams: entering inputs (1) Stream HS1 (geofluid) entering the evaporator: mass flow rate, temperature, pressure and composition Stream AIR1 (air) entering the air cooled condenser: mass flow rate, temperature, pressure and composition 70
Streams: entering inputs (2) Stream WF1 (working fluid) entering the feed pump: mass flow rate, pressure and vapor fraction Note that WF1 is a tear stream 71
Blocks: entering inputs (1) Preheater: saturated liquid conditions at outlet Vaporizer: minimum temperature difference at inlet (Dtpp) 72
Blocks: entering inputs (2) Pump: outlet pressure and hydraulic efficiency Turbine: outlet pressure and isentropic efficiency 73
Ensuring convergence: definition of the tear streams Streams WF1 and HS2 are defined as tear streams If not defined as tear stream Aspen Plus cannot find a solution 74
Design specification to guarantee a minimum superheating at turbine inlet Variables definition: temperature, dew point temperature and vapor fraction at turbine inlet Specification: superheating of 2 C at turbine inlet 75
Design specification to guarantee a minimum superheating at turbine inlet Varied variable: mass flow rate of working fluid Results m WF = 93.9 kg/s 76
Calculator block to calculate the net power output Definition of variables Definition of net power output Results W NET =3608 kw 77
Sensitivity analysis: power output versus cycle high pressure Net power (kw) 3800 3700 3600 3500 3400 3300 3200 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Pump outlet pressure (bar) The optimum cycle maximum pressure is around 18 bar 78
Optimization of net power output: problem definition Variable definition Objective function 79
Optimization of net power output: problem definition Definition of the «decision variables» (i.e, variables that are optimized) in the optimization problem The only decision variable in this problem is the pressure ratio of the compressor 80
Optimization of net power output: results The maximum power output is: W NET max = 3697 kw The optimum maximum pressure is: p max opt = 18,3 bar 81
Advantages of using Aspen Plus in the energy field (1) It is not necessary to write all the modeling equations because the block itself contains all the governing equations quick modeling The block diagram resembles the flow diagram of a real process/plant so the abstraction in the modeling phase is limited models are clearly understandable by different users The availability of a large database of substances possibility to model any kind of system The availability of a large set of property methods accurate evaluation of the thermodynamic and thermophysical properties reliable results 82
Advantages of using Aspen Plus in the energy field (2) The setup of design specifications, sensitivity analyses and optimization problems is user friendly (e.g., there is no need to define «for cycles» like in common programming languages) simplification Results are clearly readable and can be copied into Excel for further calculation simple post processing Multiple simulation runs can be launched from Excel using «Aspen Simulation Workbook» batch simulations It is a flexible software potentially any kind of system can be modeled 83
Disadvantages of using Aspen Plus in the energy field A solution (i.e., convergence) is achievable only by expert users when the complexity of the modeled system increases many users complain about the difficulty in getting results There are only few optimization methods (e.g., absence of genetic algorithms) in problems having local minima the solution could not be the true global minimum A library of gas and steam turbines is missing other software (like Thermoflow, Ebsilon, IPSEpro, etc.) are more oriented to modeling power plants compared to Aspen Plus There are not libraries for many renewable energy plant components (e.g., solar collectors, digesters, etc.) these require a user model generally written in the Fortran language 84
Appendix: Enthalpy Calculation (1) The Enthalpy reference state used by Aspen Plus for a compound is that of the constituent elements in their standard states at 298.15 K and 1 atm. Because of this choice of reference state, the actual values of enthalpy calculated by Aspen Plus may be different from those calculated by other programs (e.g., EES) All enthalpy differences, however, should be similar to those calculated by other programs 85
Appendix: Enthalpy Calculation (2) The enthalpy of a compound at a given temperature and pressure is calculated as the sum of the following three quantities: 1. Enthalpy change involved in reacting the elements at 298.15 K and 1 atm at their reference state (vapor, liquid or solid) conditions to form the compound at 298.15K and ideal gas conditions. This quantity is the enthalpy of formation 2. Enthalpy change involved in taking the compound from 298.15 K and 1 atm to system temperature still at ideal gas conditions 3. Enthalpy change involved in taking the compound to system pressure 86
Appendix: Enthalpy Calculation (3) (AspenTech Training Manual) 87
Thank you for your attention 88